Robinson was 30-for-32 passing to set an NCAA mark for completion percentage (minimum 30 completions).
Robinson's 93.8 completion percentage eclipsed the mark set by BYU's Steve Sarkisian against Fresno State in 1995. Sarkisian, now the head coach at Washington, was 31-of-34 for 91.2 percent.
Robinson, who threw for 319 yards and a touchdown, also tied a 45-year-old Troy school record with 20 consecutive completions and became the Sun Belt Conference's career leader in passing yards and completions.
"I'll think about it when I graduate," Robinson said. "Right now, I'm just happy to get a win."
The Trojans rallied from a 14-point fourth-quarter deficit, tying it on a 1-yard run by backup quarterback Deon Anthony with 3:17 remaining.
UAB had the first overtime possession and botched the snap on a 37-yard field goal attempt. On Troy's first overtime play, Anthony had a 16-yard run. Two plays later, Scott won it.
"I was proud of the way we rallied," Troy coach Larry Blakeney said. "I'm proud of the way we came back. That's a tough UAB team and I'm proud of how we rebounded."
Nelson totaled 367 all-purpose yards to set a UAB school record and scored on a school-record 97-yard kickoff return.
"We just made too many mistakes when the game was on the line," UAB coach Garrick McGee said. "I told the team that there is nobody that doesn't realize that this team is totally different from last year, and I think this team can compete for a Conference USA championship."